This question is to help you understand the idea of a sampling dis- tribution. Let X1, . . . ,Xn be IID with mean p: and variance 02. Let Yn = n'l 221:1 Xi. Then 7n is a statistic, that is, a function of the data. Since 7\" is a random variable, it has a distribution. This distri bution is called the sampling distribution of the statistic. Recall from Theorem 3.17 that 113(7\") : p. and V(7n) : 02/?1. Don't confuse the distribution of the data fx and the distribution of the statistic ff\". To make this clear, let X1, . . . ,Xn N Uniform(0,1). Let f\\ be the density of the Uniform((), 1). Plot f3. Now let YR : 711 2:1 Xi. Find 1&7\") and WHY\"). Plot them as a function of n. Interpret. New simulate the distribution of in for n = 1, 5, 25, 100. Check that the simulated values of lE(Xn) and V(Xn) agree with your theoretical calculations. What do you notice about the sampling distribution of X\" as it. increases